I found it in my online Korean dictionary. But the example phrase does not originate from it but from Oxford. I could notice this because there is Korean translation for Oxford in parenthesis http://endic.naver.com/popManager.nhn?m=search&query=on
Your post adds no light to the problem. What is it precisely that concerns you about the dictionary entry? It seems to me to be offering three examples for 'on a... basis', that is all.
Well, usually, I have thought when /(forward slash) comes, that means the same category but different character. I mean since it has three examples divided by slashes, I thought on a daily and day to day are different.
No, I think the forward slash is used to separate different common instances, whether they are synonymous or not. In this case, the 2 are synonymous but the structures are a little different, so the dictionary thought it of value to present both as examples.